nlogL = gumbellike (params, x) returns the negative log likelihood of the data in x corresponding to the Gumbel distribution (also known as the extreme value or the type I generalized extreme value distribution) with (1) location parameter mu and (2) scale parameter beta given in the two-element vector params.

[nlogL, acov] = gumbellike (params, x) also returns the inverse of Fisher’s information matrix, acov. If the input parameter values in params are the maximum likelihood estimates, the diagonal elements of acov are their asymptotic variances.

[…] = gumbellike (params, x, censor) accepts a boolean vector, censor, of the same size as x with 1s for observations that are right-censored and 0s for observations that are observed exactly. By default, or if left empty, censor = zeros (size (x)).

[…] = gumbellike (params, x, censor, freq) accepts a frequency vector, freq, of the same size as x. freq typically contains integer frequencies for the corresponding elements in x, but it can contain any non-integer non-negative values. By default, or if left empty, freq = ones (size (x)).

The Gumbel distribution is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This version is suitable for modeling maxima. For modeling minima, use the alternative extreme value likelihood function, evlike.

Further information about the Gumbel distribution can be found at https://en.wikipedia.org/wiki/Gumbel_distribution

See also: gumbelcdf, gumbelinv, gumbelpdf, gumbelrnd, gumbelfit, gumbelstat, evlike

Source Code: gumbellike